12,346 research outputs found
On the Irresistible Efficiency of Signal Processing Methods in Quantum Computing
We show that many well-known signal transforms allow highly efficient
realizations on a quantum computer. We explain some elementary quantum circuits
and review the construction of the Quantum Fourier Transform. We derive quantum
circuits for the Discrete Cosine and Sine Transforms, and for the Discrete
Hartley transform. We show that at most O(log^2 N) elementary quantum gates are
necessary to implement any of those transforms for input sequences of length N.Comment: 15 pages, LaTeX 2e. Expanded version of quant-ph/0111038. SPECLOG
2000, Tampere, Finlan
Random quantum channels I: graphical calculus and the Bell state phenomenon
This paper is the first of a series where we study quantum channels from the
random matrix point of view. We develop a graphical tool that allows us to
compute the expected moments of the output of a random quantum channel. As an
application, we study variations of random matrix models introduced by Hayden
\cite{hayden}, and show that their eigenvalues converge almost surely. In
particular we obtain for some models sharp improvements on the value of the
largest eigenvalue, and this is shown in a further work to have new
applications to minimal output entropy inequalities.Comment: Several typos were correcte
Probabilistic Models over Ordered Partitions with Application in Learning to Rank
This paper addresses the general problem of modelling and learning rank data
with ties. We propose a probabilistic generative model, that models the process
as permutations over partitions. This results in super-exponential
combinatorial state space with unknown numbers of partitions and unknown
ordering among them. We approach the problem from the discrete choice theory,
where subsets are chosen in a stagewise manner, reducing the state space per
each stage significantly. Further, we show that with suitable parameterisation,
we can still learn the models in linear time. We evaluate the proposed models
on the problem of learning to rank with the data from the recently held Yahoo!
challenge, and demonstrate that the models are competitive against well-known
rivals.Comment: 19 pages, 2 figure
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